Infix to postfix conversion

1
Infix to postfix conversion

• Process the tokens from a vector infixVect of
  tokens (strings) of an infix expression one by
  one
• When the token is an operand
• Add it to the end of the vector postfixVect of
  token (strings) that is used to store the
  corresponding postfix expression
• When the token is a left or right parenthesis or
  an operator
• If the token x is (
• Push the token x onto the stack
• if the token x is )
• Repeatedly pop a token y from the stack and
  push_back that token y to postfixVect until (
  is encountered in the end of the stack. Pop (
  from the stack.
• If the stack is already empty before finding a
  (, this expression is not a valid infix
  expression.
• if the token x is a regular operator
• Step 1 Check the token y currently on the top of
  the stack.
• Step 2
• If (i) the stack is not empty, (ii) y is not
  ( and (iii) y is an operator of higher or
  equal precedence than that of x,
• then pop the token y from the stack and
  push_back the token y to postfixVect, and repeat
  Step 1 again
• else push the token x onto the stack.
• When all tokens in infixVect are processed as
  described above, repeatedly pop a token y from
  the stack and push_back that token y to
  postfixVect until the stack is empty.

2
Infix to postfix conversion
infixVect
( 1 2 3 ) 4 ( 5 6 )
postfixVect
3
Infix to postfix conversion
stack
infixVect
( 1 2 3 ) 4 ( 5 6 )
postfixVect
(
4
Infix to postfix conversion
stack
infixVect
( 1 2 3 ) 4 ( 5 6 )
postfixVect
1
(
5
Infix to postfix conversion
stack
infixVect
( 1 2 3 ) 4 ( 5 6 )
postfixVect
1

(
6
Infix to postfix conversion
stack
infixVect
( 1 2 3 ) 4 ( 5 6 )
postfixVect
1 2

(
7
Infix to postfix conversion
stack
infixVect
( 1 2 3 ) 4 ( 5 6 )
postfixVect
1 2
-
(
8
Infix to postfix conversion
stack
infixVect
( 1 2 3 ) 4 ( 5 6 )
postfixVect
1 2 3
-
(
9
Infix to postfix conversion
stack
infixVect
( 1 2 3 ) 4 ( 5 6 )
postfixVect
1 2 3 -
10
Infix to postfix conversion
stack
infixVect
( 1 2 3 ) 4 ( 5 6 )
postfixVect
1 2 3 -

11
Infix to postfix conversion
stack
infixVect
( 1 2 3 ) 4 ( 5 6 )
postfixVect
1 2 3 - 4

12
Infix to postfix conversion
stack
infixVect
( 1 2 3 ) 4 ( 5 6 )
postfixVect
1 2 3 4
-
13
Infix to postfix conversion
stack
infixVect
( 1 2 3 ) 4 ( 5 6 )
postfixVect
1 2 3 4
(
-
14
Infix to postfix conversion
stack
infixVect
( 1 2 3 ) 4 ( 5 6 )
postfixVect
1 2 3 4 5
(
-
15
Infix to postfix conversion
stack
infixVect
( 1 2 3 ) 4 ( 5 6 )
postfixVect
1 2 3 4 5

(
-
16
Infix to postfix conversion
stack
infixVect
( 1 2 3 ) 4 ( 5 6)
postfixVect
1 2 3 4 5 6

(
-
17
Infix to postfix conversion
stack
infixVect
( 1 2 3 ) 4 ( 5 6 )
postfixVect
1 2 3 4 5 6
-
18
Infix to postfix conversion
stack
infixVect
( 1 2 3 ) 4 ( 5 6 )
postfixVect
1 2 3 4 5 6